One of the biggest frustrations for the consumer electronics industry is that cu

Question

One of the biggest frustrations for the consumer electronics industry is that customers are accustomed to returning goods for any reason. Recently, it was reported that returns for "no trouble found" were 68% of all returns. Consider a sample of 25 customers who returned consumer electronics purchases. Use the binomial model to answer the following questions: a. what is the probability that exactly 12 of the 25 customers made a return for "no trouble found"? b. what is the probability that up to 14 (0 through 14) of the customers made a return for "no trouble found"? c. what is the probability that 17 or more customers made a return for "no trouble found"? One of the biggest frustrations for the consumer electronics industry is that customers are accustomed to returning goods for any reason. Recently, it was reported that returns for "no trouble found" were 68% of all returns. Consider a sample of 25 customers who returned consumer electronics purchases. Use the binomial model to answer the following questions: a. what is the probability that exactly 12 of the 25 customers made a return for "no trouble found"? b. what is the probability that up to 14 (0 through 14) of the customers made a return for "no trouble found"? c. what is the probability that 17 or more customers made a return for "no trouble found"?

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
P( X = 12 ) = ( 25 12 ) * ( 0.68^12) * ( 1 - 0.68 )^13
= 0.0188

b)
P( X < = 14) = P(X=14) + P(X=13) + P(X=12) + .....+ P(X=1) + P(X=0)
= ( 25 14 ) * 0.68^14 * ( 1- 0.68 ) ^11 + ( 25 13 ) * 0.68^13 * ( 1- 0.68 ) ^12 + ......... +( 25 0 ) * ( 0.68^0) * ( 1 - 0.68 )^25

= 0.1424

c)

P( X > = 17 ) = P( X=17) + P(X=18) ... P(X=25) = 0.5943

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